Final answer:
Using the pattern provided, it appears that the runner would not fit the running total of 372 miles within the options of 4, 5, 6, or 7 days since the given daily distances when followed properly do not align with any of the choices. There could be a need to reassess the calculations or examine the distances for a possible error.
Step-by-step explanation:
To find out how many days it took the runner to run a total of 372 miles, we need to establish the pattern of the running sequence. The runner runs 15.5 miles and then runs twice that distance the next day, and this pattern repeats itself. Therefore, over two days the runner covers 15.5 miles + (2 × 15.5 miles) = 15.5 miles + 31 miles = 46.5 miles.
The next step is to determine how many full cycles of two days it takes to reach or surpass the total distance of 372 miles:
- Total distance over two days: 46.5 miles
- Now, we divide the total distance run by the runner by the sum of distances run in two days: 372 miles / 46.5 miles per two days = 8 cycles
- Therefore, in 8 cycles of two days, the runner would run 8 × 46.5 miles = 372 miles.
- Since each cycle consists of 2 days, the total days it takes is 8 × 2 = 16 days. This exceeds the options provided, indicating a need to reassess our calculations.
- However, if we look closely, the question might actually involve partial cycles, meaning the runner might surpass the total distance required before completing an entire cycle. Let's calculate day by day:Day 1: 15.5 miles
- Day 2: 31 miles (2 × 15.5)
- Day 3: 15.5 milesDay 4: 31 miles (2 × 15.5)If we add these up, we get 15.5 + 31 + 15.5 + 31 = 93 miles in four days. Repeating this pattern four times:4 days × 93 miles = 372 miles in 16 daysTherefore, there seems to be a misinterpretation of the distances involved or an error in the initial conditions as neither the distances nor the days align with the multiple-choice options provided in the original question.